Rigidity factor of mat foundation-Joseph Bowles 1

[ramihabchi]

Can someone please answer the questions in the attached picture?
I am trying to understand how to use the rigidity factor equation, and I need to know how columns are taken into account in rigidity of mat and combined footing according to Bowles.
tried to search the web but in vain.

 

[KootK]

The EI_bi term is intended to account for the flexural rigidity that the superstructure adds to the mat. In practical terms, I believe that it's supposed to wind up being the sum of the rigidities of all of the beams above a given location on your design strip that you feel would be encouraged to flex and take on a curvature roughly matching that of your mat. Columns would contribute to this modestly but I believe that the intent is for the designer to omit their contribution for simplicity.

You would only include slabs in the EI_bi term if you felt that they were capable of stiffening the mat in a manner similar to how beams would. I would not normally expect to include slabs in this. Perhaps if we were talking about a thick transfer slab etc.

If you want to include the columns (a sort of vierendeel truss action), it might be expedient to tackle the problem by modelling the setup instead of using the equation. The equation is obviously pretty rough stuff.

 

[ramihabchi]

@KOOTK,
What about the rigidity term of walls.is there any minimum dimension for wall to be considered in the calculation? there are no inclusion for the length of the wall, only height and thickness..

 

[KootK]

The inclusion of the wall term has never made much sense to me. To be effective, a wall would need to run the full length of the building or, at the least, several framing bays. As you know, walls of that sort are pretty rare on the interior of a building. They'll occur at the perimeter in certain situations but, then, I would be tempted to say that the wall replaces the stiffness of the raft rather than augments it.